RKD STUDIES

Previous analysis of a subset of Vermeer’s paintings revealed three weave matches: The Lacemaker (L29) and Young Woman Seated at a Virginal (L36); Young Woman Standing at a Virginal (L33) and Young Woman Seated at a Virginal (L34); Woman with a Lute (L14) and Woman Writing a Letter, with Her Maid (L31).¹ More recently, the consideration of two Vermeer paintings, The Geographer (L27) and The Astronomer (L28),² proposed by Walter Liedtke and others as a pendant pair, revealed a fourth weave match among Vermeer’s 34 paintings on canvas catalogued in Liedtke’s 2008 catalogue of Vermeer’s paintings.³ Our continuing examination of weave maps of the complete set of X-radiographs of all of Vermeer’s paintings reveals the fifth, Woman with a Pearl Necklace (L18) and Woman Holding a Balance (L19), and sixth, Woman with a Lute (L14) and Woman with a Pearl Necklace (L18), matches, which are described here. The route to their discovery will be used as an illustration of how a collection of weave maps of paintings on canvas by an artist can be used to assess and exploit their use of canvas from the same roll for pendants or a series of paintings.

The process of finding weave matches begins with identification of all of the paintings that exhibit count matches. A count match occurs when the average thread counts in the two thread directions are a close match between two paintings. The tolerance for a match as less than 1 thread/cm difference in the warp threads and less than a bit more than 1 thread/cm for weft threads has been proposed for seventeenth-century canvases.⁴ Here, as discussed in the previous chapter,⁵ spectral methods are used to estimate the frequency of the principal sinusoidal component of the Fourier decomposition in regions of interest, and the principal component’s frequency serves as a proxy for the actual thread count.⁶

If we examine the average ‘thread counts’ for each painting in table [1] we can produce pairings that are reasonable to be considered count matches.⁷ The measure used at this point is that the average thread counts differ by no more than 1 thread/cm in one direction and by no more than 2 threads/cm in the other direction.

Table 1
Average of the Principal Sinusoidal Component Frequency (threads/cm) Across the Patches Evaluated Covering the Full Painting (from 0.5 cm evaluation squares centered on 0.25 cm grid).

Thus, all painting locations captured by a rectangle 1 thread/cm high and 2 threads/cm wide would be count matches of each other.  An orange box of these dimensions captures Woman with a Lute (L14), Woman with a Pearl Necklace (L18), Woman with a Balance (L19), and Woman Writing a Letter, with Her Maid (L31) as count matches of each other.  Alternatively, all painting locations within a tall rectangle 1 thread/cm wide and 2 threads/cm tall would also be considered count matches. Such a tall blue rectangle encloses Young Woman Reading a Letter (L05), View of Delft (L12), Woman at the Virginal with a Gentleman (L15), The Lacemaker (L29), and The Love Letter (L30) as count matches of each other.

While a count match does not imply a weave pattern match, a weave pattern match is implausible without a count match. Computational methods exist for assessing the degree of weave pattern match between the weave maps of two paintings, which can narrow down the search for weave matches.⁸ For the first three matches discovered,⁹ a computational approach was used, along with observations that the canvases of paintings of interest appeared quite similar, for example as for The Lacemaker (L29) and Young Woman Seated at a Virginal (L36).¹⁰ Here, we will illustrate a process of directing our search for weave matches using the information in table 1 and the weave maps produced by the computational methods described in the previous chapter.¹¹

Begin by comparing each of the paintings in table 1 to all of the other paintings in table 1 to see if a horizontal-to-horizontal-plus-vertical-to-vertical match is within our assigned range of a count match if the horizontal threads were in the warp direction. Repeat for the assumption that the horizontal threads are in the weft direction. The same count match test is done in the cross-direction comparison of horizontal-to-vertical plus-vertical-to-horizontal.

1
Average Thread Counts of 34 Vermeer Paintings on Canvas from table 1 plotted by locating the larger thread count on the vertical axis and the smaller thread count on the horizontal axis. An orange rectangle encloses a group of count matching canvases with the larger thread counts within a range of 1 thread/cm and the smaller within a range of 2 threads/cm. A blue rectangle encloses a group of count matching canvases with the larger thread counts within a range of 2 threads/cm and the smaller within a range of 1 thread/cm (the adjacent numbers are the L numbers following [Liedtke 2008]).

Each member of the group of four – Woman with a Lute (L14), Woman with a Pearl Necklace (L18), Woman Holding a Balance (L19), and Woman Writing a Letter, with Her Maid (L31) – enclosed in the orange rectangle in figure [1] has a count match with every other member within the orange rectangle according to the rule that they are no more than 1 thread/cm different in one thread direction and less than 2 threads/cm apart in the other. Incidentally, they are also the only paintings with the thread count in one direction over 20 threads/cm.¹² For each painting in this group of four, its three count matches are with the other three paintings in this group of four. Three of the paintings – Woman with a Lute (L14), Woman with a Pearl Necklace (L18), and Woman Holding a Balance (L19) – have horizontal-horizontal-plus-vertical-vertical count matches with each other and these three have cross-direction horizontal-vertical-plus-vertical-horizontal count matches with Woman Writing a Letter, with Her Maid (L31). Interestingly, the match of Woman with a Lute (L14) horizontal to Woman Writing a Letter, with Her Maid (L31) vertical illustrated in figure 6 in §5.5.4, is one of the first three Vermeer weave matches reported.¹³ The weave maps for Woman with a Lute (L14), Woman with a Pearl Necklace (L18), Woman with a Balance (L19), and Woman Writing a Letter, with Her Maid (L31) appear in figures [2-5].

Directly comparing the weave density patterns in figures 2-5 is misleading as in these figures the maps are scaled to be the same size in one dimension, while the paintings are not. One approach to examining pairs at their actual relative size is to use the function align, which was described in the preceding chapter.¹⁴ This software puts the properly-sized weave maps of the pair being examined for a weave match on screen and allows rotations and flips and translation in an attempt to visually test the possibility of a weave match. This approach was used to reveal a weave match between the horizontal thread weave density maps of Woman with a Pearl Necklace (L18) and Woman Holding a Balance (L19), as illustrated in figure [6].

The advantage of align is that it re-draws the color-coded weave maps of, for example, Woman with a Pearl Necklace (L18) and Woman Holding a Balance (L19) in figure 3 and figure 4, each of which has its own distinct color bar centered around its own map’s average thread count, to the samecolor bar. The averages of the thread counts for Woman with a Pearl Necklace (L18) and Woman Holding a Balance (L19) in the horizontal direction differ by just over ½ thread/cm, but this effects the sharpness of the visual similarity of the two weave patterns. Compare the relevant images in figures 3, 4, and 6.

However, the images, such as in figures 2-5 that arise with displayWeaveMaps from the previous chapter, despite modest differences in the average thread count translating into modest distinctions in the color bars for the same thread count, can prove quite useful in a slightly less sophisticated procedure.¹⁵ The initial step is to compile a collection (such as allVermeerMaps.pdf) of images containing all of the horizontal and vertical weave maps for all 34 of Vermeer’s paintings on canvas with the maps at the relative size appropriate to each painting. Extracting individual maps and placing them in a paint program that allows their rotation and flipping and movement aids visual matching of stripe patterns in aligned maps, which was done to construct figure [7].

This quartet includes the sixth weave match pair (Woman with a Lute (L14)-Woman with a Pearl Necklace (L18)) discovered among Vermeer’s canvases. The four paintings are shown in their original orientation as canvas rollmates in figure [8].

The arrangement in figure 7 suffers from some ambiguity. The relative position of each thread-sharing pair could conceivably be reversed. For example, the horizontal thread density map of Woman with a Lute (L14) could be positioned above the vertical thread density map of Woman Writing a Letter, with Her Maid (L31) and maintain a viable weave match, as shown in figure 5 in §5.4.3.¹⁶ This would rearrange the weave maps in the right half of figure 7 so the pair Woman Writing a Letter, with Her Maid (L31) and Woman Holding a Balance (L19) in the quartet would be horizontally aligned. But, the corresponding density maps do not appear to match. Plus, the difference of 1.74 in the average thread counts in what would be the shared direction, that is horizontal for Woman Writing a Letter, with Her Maid (L31) and vertical for Woman Holding a Balance (L19), from table 1 is large for a count match. Therefore, the combination of the four paintings in figure 7 is at least as long as the height of Woman Writing a Letter, with Her Maid (L31) plus the sum of the widths of Woman with a Pearl Necklace (L18) and Woman Holding a Balance (L19), which is over 160 cm. The group width, which is the sum of the heights of Woman with a Lute (L14) and Woman with a Pearl Necklace (L18), is around 100 cm, which is approximately 1.5 el, a standard strip width.¹⁷

One observation regarding the six weave-matched pairs, three of which appear in figure 7, is how close the thread count match is in both directions, with the thread-sharing direction being the closer fit, as apparent from table 2 where the matching pairs are listed in their order of discovery. This suggests further searching among pairs of paintings for count matches where both directions are within 1 thread/cm of each other.

Recognizing that so many of Vermeer’s canvases have thread counts with an integer portion of 14 threads/cm, consider canvases where counts in both directions are between 14 and 15 threads/cm, and thus within 1 thread/cm of each other. The resulting trio of Officer and Laughing Girl (L06), Young Woman with a Wine Glass (L10), and Girl with a Pearl Earring (L22) have thread counts in both directions between 14.38 and 14.86. One ‘almost-but-not-quite’ weave match that emerges, illustrated in figure [9], aligns Officer and Laughing Girl (L06) and Young Woman with a Wine Glass (L10) vertically. An orientation matching Girl with a Pearl Earring (L22) to either Officer and Laughing Girl (L06) or Young Woman with a Wine Glass (L10) is not obvious. This confirms that the choice of a threshold of 1 thread/cm for the thread count difference in both directions between two canvases need not be a feature that always leads to a weave match.

But, since the 1 thread/cm difference threshold for both thread directions has proven quite useful, we will suggest those pairs with count matches that satisfy this tight threshold as prime candidates for continuing the hunt for rollmates among Vermeer’s paintings on canvas. Table 3 lists the tighter count matches for each painting.

6
Fifth Weave Match Pair Among Vermeer’s Paintings on Canvas: Horizontal thread weave density maps of Woman with a Pearl Necklace (left) and Woman Holding a Balance (right) (from 0.5 cm evaluation squares centered on 0.25 cm grid).

7
Matching Weave Maps of a Gang of Four: Woman Writing a Letter, with Her Maid upper left, Woman with a Lute below Woman Writing a Letter with Her Maid, Woman with a Pearl Necklace to right of Woman with a Lute, Woman Holding a Balance below Woman with a Pearl Necklace (from 0.5 cm evaluation squares centered on 0.25 cm grid).

8
Four Paintings (Woman with a Lute, Woman with a Pearl Necklace, Woman Holding a Balance, and Woman Writing a Letter, with Her Maid) in Weave-Matching Orientation.

Table 2
Count Match Fits of Known Weave Matches.

The scatter plot in figure [10] provides relative locations and examples of 3 square boxes enclosing all tight count matches of the painting located at the center of the box, that is an orange square centered on Diana and Her Nymphs (L01) encloses no count matches to Diana and Her Nymphs (L01); a green box centered on The Love Letter (L30) includes The Letter Reader (L05), View of Delft (L12), Woman at the Virginal with a Gentleman (L15), A Lady Writing (L20), and The Lacemaker (L29); and a blue box centered on The Guitar Player (L35) encloses Mistress and Maid (L21), Young Woman Standing at a Virginal (L33), and Young Woman Seated at a Virginal (L34).

In table 3 the parenthetical notation (C) corresponds to a cross-match in counts associating the horizontal count in one painting with the vertical count in the other one (and the vertical with the horizontal). The notation (B) indicates that both the regular horizontal-horizontal-plus-vertical-vertical pairing and the cross-pairing of horizontal-vertical-plus-vertical-horizontal are count matches with no more than a 1 thread/cm difference in both directions. No notation indicates a horizontal-horizontal-plus-vertical-vertical pairing. The close count matches among known weave matches are underlined.

The scatter plot in figure [11] encloses in red rectangles the four groups of count matches, which are typically pairs, discovered so far.

In addition to the three pairwise matches in the group of four as shown in figures 7 and 8, the other three pairwise weave matches and their associated paintings in their original orientation are shown in figures [12-14].

Table 3 lists 79 pairs with close count matches. Each pair is listed twice: once in the close count matches of partner number 1 and again in the close count matches of partner number 2. As noted earlier, all six ‘known’ weave match pairs appear in this group of close count match pairs. That’s just six out of 79 prime candidates. Are there more?

To help facilitate more precise weave match hunting, Appendix IV in this RKD Studies publication contains separate images of the weave density maps of each painting in table 3 and its associated group of close count matches. For example, consider figure [15].

For the match candidate in each row below the top one, the first two figures should be compared to the horizontal weave map in the top row. This comparison will require movement of the candidate weave map to test alignment. The second two figures in the match candidate row are to be compared to the vertical weave map in the top row. Only one (or none) of these 4 match tests can exhibit aligned stripes. In figure 15 (as shown in figure 7), the first entry in the third row can be aligned to the right of the first image of the top row and the third entry in the second row can be aligned below the second entry in the top row. The second entries in rows 2 and 3 are dark because the center of the color bar is the average horizontal thread count of Woman with a Pearl Necklace (L18), that is 20.73, which is greater than the average vertical thread counts of Woman with a Lute (L14) and Woman Holding a Balance (L19). Similarly, the fourth entries in rows 2 and 3 are lighter because the center of the color bar is the average vertical thread count of Woman with a Pearl Necklace (L18), that is 15.88, which is less than the average horizontal thread counts of Woman with a Lute (L14) andWoman Holding a Balance (L19). These images of the weave maps of the count matches listed for each Vermeer painting in table 3 can be cut apart and readily shifted relative to the image in the top row as a weave match check.

To close this section we reiterate the point that attribution relies on multiple features, including paint material and support material analysis. Plus, the lack of a count or weave match with any of the paintings in table 1 is a neutral feature regarding attribution to Vermeer. As table 1 indicates, Diana and Her Nymphs (L01), Christ in the House of Martha and Mary (L02), and The Art of Painting (L26) have no count matches among Vermeer’s paintings.

14
Matching Weave Maps - Left: Young Woman Standing at a Virginal, Right: Young Woman Seated at a Virginal.

15
Weave Maps Woman with a Pearl Necklace and its Close Count Matches Scaled to Relative Size (The top row includes the horizontal (left) and vertical (right) weave density maps for the painting to which matches are being considered. The subsequent rows each include four images: (i) the horizontal thread density map of the match candidate with the center of its color scale matching that of the horizontal weave map in the top row, (ii) the vertical weave map of the match candidate rotated 90 degrees and color-centered on the color scale of the horizontal weave map in the top row, (iii) the vertical weave map of the match candidate color-centered on the color scale of the vertical weave map in the top row, and (iv) the horizontal weave map of the match candidate rotated 90 degrees and color-centered on the color scale of the vertical weave map in the top row.)